NEET 2021 · PhysicsQuality factorPrevious Year Question
A series LCR circuit containing 5.0 H inductor, 80 μF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:
Answer: (A) 46 rad/s and 54 rad/s. Answer: (A) 46 rad/s and 54 rad/s Solution: Resonant angular frequency ω₀ = 1/√(LC) = 1/√(5.0 × 80×10⁻⁶) = 1/√(4×10⁻⁴) = 50 rad/s.
- A.46 rad/s and 54 rad/s✓
- B.42 rad/s and 58 rad/s
- C.25 rad/s and 75 rad/s
- D.50 rad/s and 25 rad/s
Correct Answer
(A) 46 rad/s and 54 rad/s
Solution & Explanation
Answer: (A) 46 rad/s and 54 rad/s Solution: Resonant angular frequency ω₀ = 1/√(LC) = 1/√(5.0 × 80×10⁻⁶) = 1/√(4×10⁻⁴) = 50 rad/s. Bandwidth (full width at half power) Δω = R/L = 40/5 = 8 rad/s. The two half-power angular frequencies are ω₀ ± Δω/2 = 50 ± 4 = 46 rad/s and 54 rad/s.
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